Improved Hessian Method in Global Analysis of Parton Distribution Functions

Abstract

The Hessian method is widely applied in the global analysis of parton distribution functions (PDFs), which uses a set of orthogonal eigenvectors to give predictions of a physical observable. Its uncertainty is estimated based on the assumption that all physical observables can be approximately expressed as linear functions of the non-perturbative parameters in PDF. In this article, we report an improved Hessian method which takes the non-linear effects into account in the uncertainty estimation. A pseudo global analysis is designed to numerically test the new method. The non-linear uncertainties can significantly enlarge the original linear ones. Such uncertainties can be reduced with high precision data introduced into the global analysis. However, the non-linear effect could still be sizable corresponding to the current precision of the experimental measurements.